Chapter SR4, Problem 67P

Solution

To simplify the expression $\frac{1}{2}+\frac{3}{5}-\frac{1}{4}$ .

  $\frac{17}{20}$

Given:

The expression, $\frac{1}{2}+\frac{3}{5}-\frac{1}{4}$.

Concept Used:

To add or subtract fractions with unlike denominators, follow the below steps:

Step 1: Find the least common multiple (LCM) for the denominators.

Step 2: Multiply the numerator and denominator to get like denominators.

Step 3: Turn the other fractions into equivalent fractions.

Step 4: Add the numerators over the common denominator.

Step 5: Simplify and reduce the answer if necessary.

Calculation:

In order to simplify the given expression, note that the least common multiple of 2, 5, and 4 is 20. So, make all denominators equal to the LCM and combine the numerators over the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{1}{2}+\frac{3}{5}-\frac{1}{4}=\frac{1}{2}\cdot \frac{10}{10}+\frac{3}{5}\cdot \frac{4}{4}-\frac{1}{4}\cdot \frac{5}{5}\\ =\frac{10}{20}+\frac{12}{20}-\frac{5}{20}\\ =\frac{10+12-5}{20}\\ =\frac{17}{20}\end{array}$

Thus, the simplified expression is $\frac{17}{20}$ .